This has gone on long enough, and since it's stopped raining cats and dogs (for now), the points are no longer soggy. Time to reveal the answer.

The question:
Did you know that the base dimensions of the Great Pyramid of Giza are a function of Pi? Why would a square footprint be a function of Pi?

I gave a couple of hints, the last one was the biggest; the point that the ancients had no linear measuring tool that could account for the precision of the base dimensions. The key distinction is linear measurement tool, as in a tape, or stick, which would be too variable over such great lengths.

While there is no definitive evidence of how the pyramids were laid out (they left few records of how they were constructed). It's been suggested that they employed a rolling ruler. In other words, a wheel on a stick. To measure the distance, they rolled the wheel along the desired track and simply counted the revolutions. This results in a very precise measurement.

Since the circumference of any circle is a function of Pi, multiple revolutions of the wheel are also a function of Pi, and totally coincidental to the design of the base.

See, I told you it was simple.

The points are still mine. Tom

_________________"There is no path to peace, peace is the path."Mohandas K. Ghandi

TMS: EXCELLENT ! ! ! Rumageing around in those dark recesses brings to mind that they (Egyptian site managers) may have used a system of range poles to establish a line and then used a divider type contraption to "walk out" the distance required. The spread of the divider points being equal to the accepted unit of lenngth they chose to use.

Hmm. Logical except for one thing. Pyramids were also built by other cultures such as the Mayans, who did not have the wheel from what I understand. So would the same coincidental relationship hold for those? And if so, lacking a rolling ruler, how did they do it?

I don't know if the bases of the Mayan pyramids have a relationship to Pi, or their degree of precision. As you say, a comparison might be in order.

Tom

The mind tends to wander occasionally. This got me thinking about ancient Metrology. Not much info about it that a couple hours of web surfing could dig up, and nothing that I could find regarding the Americas (except for the Mayan calendar thing). Most of the web info deals with Mediterranean area civilizations, and some Chinese info.

Standardized measurement systems for distances, weights, etc. had to have been in place (even tho different for different cultures ) for nearly anything to have been constructed, and for trade to have been carried out.

So what was the radius or diameter or circumference of the wheel? Was it standardized for all building projects or just used for a particular building/ pyramid? If it was a standard diameter across the area or time period, then it could be recognized as a tape measure wouldn't it? At any rate it is a measuring device of constant calibration just like a tape measure in my mind so how can you connect pi to the measurement of the base of a pyramid? A person could reverse engineer a wheel to equal a yard and do the same thing. In fact they have!!

Rog

_________________Dont badmouth no strangers, they just friends you aint met yet.

An ounce of responsibility is worth a pound of State and Federal laws.

I spent most of my money on woodworking
tools and beer, the rest I just wasted.

Over the distances of the base dimensions of the great pyramids, even a modern material tape would not be precise enough to match the "as built" precision. The materials they had four thousand years ago would be even less consistent.

A tape stretches and shrinks with temperature, strain, and in the case of organic materials, humidity. The rolling ruler is so precise because it is less effected by these factors.

It makes no difference what size wheel was used, or if it was ever used for anything else. The fact that it was a circle makes the distance covered by the circumference a function of Pi, and multiples of that distance would still be a function of Pi.

Tom

_________________"There is no path to peace, peace is the path."Mohandas K. Ghandi

Over the distances of the base dimensions of the great pyramids, even a modern material tape would not be precise enough to match the "as built" precision. The materials they had four thousand years ago would be even less consistent.

A tape stretches and shrinks with temperature, strain, and in the case of organic materials, humidity. The rolling ruler is so precise because it is less effected by these factors.

It makes no difference what size wheel was used, or if it was ever used for anything else. The fact that it was a circle makes the distance covered by the circumference a function of Pi, and multiples of that distance would still be a function of Pi.

Tom

I wonder if the Pharaoh reminded them to keep their wheels inflated to the proper psi?

An interesting question. Is there any proof beyond supposition that a wheel was the measuring tool? It seems logical considering what was available at the time, but there are some faults with it.

The immediate one that comes to mind is the measuring lines would have to be equally uniform and straight. That is, no ups and downs on each line, and each line has to be parallel to the opposite one. Perhaps difficult to achieve over long distances with the tools available. Second- the same wheel must be used for all measurements since wheel production is probably not standardized, and any differences would accumulate.

I suspect a block system might be equally precise compared to the wheel. If the blocks were cut to some equal size, and laid precisely, the cutting and measuring errors would tend to cancel out. So each side is equal to X blocks.

A bigger problem would be making it square since diagonal measure would have the same problems related above. Was the North star a known quantity back then?

From what I've read, which is admittedly not everything, the wheel is the only form of measurement that is precise enough to account for the 'as built' precision. Even though multiple block measurements may average out, that is accuracy, not precision. Multiples of any measurement (even the wheel) will add variability, which only accumulates.

And don't forget, that this was a question of Pi. The dimensions are multiples of Pi, which was an unknown concept at that time.

Tom

_________________"There is no path to peace, peace is the path."Mohandas K. Ghandi

Tom - I would have to disagree on the use of the wheel to achieve accuracy under the conditions which must have existed.

Theoretically, of course, the wheel is an accurate means of measuring, but in practice on the ground with small wheels it would seem doubtful that high accuracy could be obtained.

I say this with a considerable experience in measuring long distances on the ground under field conditions. Once, out of curiosity, I compared measurements on a level surface (earth dam) using a 16" wheel, a bureau of standard certified steel 300' chain, and a geodimeter using reflected light. Total distance was about 1200'.

The geodimeter and chain difference was 0.03'. The wheel difference was over 0.4'. I suspect the inaccuracy of the wheel was due to slippage even though the surface was level, machine compacted, earth. A wooden wheel on a stick achieving this accuracy on the surface which must have existed at the time would seem doubtful.

This is an interesting discussion. What other possibilities might there be - not for the PI coincidence, but the accuracy and precision of whatever might have been used to satisfy the 'as designed' geometry of any of the ancient structures/megaliths around the world. It's a topic that has been endlessy pursued for a long time, but I don't think it's been settled yet.

This is an interesting discussion. What other possibilities might there be - not for the PI coincidence, but the accuracy and precision of whatever might have been used to satisfy the 'as designed' geometry of any of the ancient structures/megaliths around the world. It's a topic that has been endlessy pursued for a long time, but I don't think it's been settled yet.

True! I would probably vote for the aliens, or laying a dedicated number of slaves head to foot.

This is an interesting discussion. What other possibilities might there be - not for the PI coincidence, but the accuracy and precision of whatever might have been used to satisfy the 'as designed' geometry of any of the ancient structures/megaliths around the world. It's a topic that has been endlessy pursued for a long time, but I don't think it's been settled yet.

True! I would probably vote for the aliens, or laying a dedicated number of slaves head to foot.

Actually, the recent thinking - at least for Egypt - is that the pyramids were not built by slaves as Hollywood portrayed it, but were paid craftsmen and laborers. That it was more of a gov't jobs plan. Kinda like the US interstate hiway system back in the day. There was a very large surrounding city that tends to support that view. Makes a lot more sense to me, since slave labor would likely be more expensive and less reliable and skilled. Much better to have enthusiastic support than reluctant obedience.

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